I've been recently looking into getting an extension tube set for some macro photograpy. I've noticed that a lot of these 3 tube sets (for Canon EOS) have the same, very specific lengths: 13mm, 21mm, and 31mm.

I've done some searching on Google as to the significance of these lengths, but have found nothing. Does anyone know why these lengths in particular seem to be so common?

1 Answer
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It might help if you thought of everything in Imperial units rather than metric. A normal lens for 35mm cameras is a 2-inch lens (50mm), and the tubes are (approximately) 1/2-inch (13mm), 3/4-inch (21mm) and 1 1/4-inch (31mm). That makes both magnification calculation and bellows draw (exposure compensation required for the lens extension) relatively easy to calculate, whether the tubes are used alone or in combination, when the lens is focused to its infinity mark. For instance, combining the 21mm and 31mm tubes would give you a 1:1 magnification ratio with a 2-stop exposure compensation.

The calculations are similarly simple for 24mm, 100-105mm and 200mm lenses, at least in a ballpark sense.

Remember that zoom lenses were once far from ubiquitous, and it was anomalous for a photographer to own a 35mm camera without also owning a 50mm lens. It might also help to remember that TTL metering was, once upon a time, and only if your camera actually had it, something you wouldn't really want to rely on most of the time (almost all metering was center-weighted, and rather depended on the condition of your camera's batteries or the age of the selenium cell).

These days we don't need to rely so much on external metering for most photography, and it's as likely as not that you'll be using a zoom lens as a prime, so maybe the tube lengths don't make as much immediate sense as they used to. But that's why millimeter lengths that are around rounded simple fractions (halves and quarters) of an inch are normal.